Holographic stereogram (HS) is a kind of hologram that can accelerate calculation, which can realize the monochromatic holographic three-dimensional (3D) display, and combining it with the color rainbow hologram and realizing the half-circle viewable color rainbow holographic 3D display which can be watched by many people have practical application value. Based on the HS calculation principle, the side angle of view and the field of view of the elemental hologram are designed, and the spectrum of the elemental hologram containing red, green, and blue information through frequency domain multiplexing is achieved. The elemental hologram is obtained by taking the real part of the complex amplitude from the inverse Fourier transform of the spectrum. The high-resolution half-circle viewable color rainbow HS can be achieved by combining all elemental holograms. A high resolution half-circle viewable color rainbow HS with a resolution of 200800 pixel×200800 pixel and a size of 64 mm×64 mm is calculated only within 15.15 min by parallel acceleration. Reflective illumination is used for optical reproduction and a clear color holographic 3D display that can be viewed by multiple people is achieved, which is expected to be applied to 3D military maps, 3D sand tables, and other fields.